Question: Simplify the following expression: $\dfrac{72r}{54r^4}$ You can assume $r \neq 0$.
$ \dfrac{72r}{54r^4} = \dfrac{72}{54} \cdot \dfrac{r}{r^4} $ To simplify $\frac{72}{54}$ , find the greatest common factor (GCD) of $72$ and $54$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $54 = 2 \cdot 3 \cdot 3 \cdot 3$ $ \mbox{GCD}(72, 54) = 2 \cdot 3 \cdot 3 = 18 $ $ \dfrac{72}{54} \cdot \dfrac{r}{r^4} = \dfrac{18 \cdot 4}{18 \cdot 3} \cdot \dfrac{r}{r^4} $ $\phantom{ \dfrac{72}{54} \cdot \dfrac{1}{4}} = \dfrac{4}{3} \cdot \dfrac{r}{r^4} $ $ \dfrac{r}{r^4} = \dfrac{r}{r \cdot r \cdot r \cdot r} = \dfrac{1}{r^3} $ $ \dfrac{4}{3} \cdot \dfrac{1}{r^3} = \dfrac{4}{3r^3} $